The magic of Primes

We all know what a prime number is. It is a number that is divisible only by 1 and itself. But do you know how fascinating these numbers are?
You could call them the building block of all numbers.

Why do I say that?
We all know numbers that are not prime numbers are called composite numbers. But you may not know that all composite numbers can be built from prime numbers in a unique way by multiplication. In fact, this fact is called the “Fundamental Theorem of Mathematics” – that any number can be written as a factor of two or more primes in a unique way (by unique I mean there is only one way to write it as a factor of primes).

So 96 can be represented as 2 * 2 * 2 * 2 * 2 * 3. There is no other way to factorize it using primes.
And this is true for all prime numbers. Isn’t it fascinating?

There are many fascinating things about prime numbers and their role as the building block for all numbers.
But let me tell you about one strange fact – there is no largest prime number. It is just not possible to have something called the “largest prime number”. A Greek Mathematician called Euclid proved it more than 2000 years ago.

There is an active search going on for finding larger and larger prime numbers. The largest one found so far is 243,112,609 ? 1. What is that? It is 2 multiplied by itself 43 million, one lakh, twelve thousand, six hundred and nine times, and one subtracted from that number. That number is 12 million digits long.
How big is that? Let me tell you – If you could write 80 numbers in a line, and your notebook page had 40 lines, and your notebook had 50 pages, it would take you 80 notebooks to write down this number. Of course, the search for still larger prime numbers continues.

Properly, it is the Fundamental Theorem of ARITHMETIC (not mathematics) and it was proven by Gauss. I'm not sure any school textbook has tackled the concept properly since Dolciani, et al in Modern Introductory Analysis (1967). The extensions of the complexities of prime numbers include the Goldbach Conjecture and the Riemann Conjecture.